"Sins not only wound or destroy our communion with God, they also compromise the inner balance of the person and her properly ordained relationship with other creatures. For a complete healing, not only are regret and forgiveness of sins necessary, but also reparation for the resulting disorder which usually continues to subsist.
In this commitment of purification the penitent is not isolated.
He is immersed in a mystery of solidarity through which the holiness of Christ and the Saints is also very useful. God communicates to him the graces deserved by others with the immense value of their existence, in order to make his reparation quicker and more effective ... The shepherds grant such a benefit to those who have the right internal dispositions and accept to perform some prescribed acts. This intervention in the penitential way is the granting of an Indulgence."
(Italian Episcopal Conference, Catechism for Adults No. 710).
Examples:
Indulgence of St Mary of the Angels (Assisi, Italy).
Indulgence of St Peter of Rome (on jubilee years).
Counter-example:
There were cases in the past of rich people paying the poor to do penance in their place: there was a trafficking of indulgence that obviously had nothing to do with a genuine solidarity with Christ and the saints.
Example:
Assisi: Saint Mary of the Angels